Vibrations
Waves Lesson 0a-d 4/29/12
vibrational motion

• resting position - equilibrium position - balance of forces
• forced vibration - describes the force which sets an otherwise resting object in motion
• damping - the tendency of a vibrating object to lose or to dissipate its energy over time
• restoring force - acts upon the vibrating object to move its back to its original equilibrium position
• vibrational motion is contrasted with translational motion

properties of periodic masses

• if it were not for dampening, the vibrations would endure forever
• periodic motion - a motion that is regular and repeating
• vibrations have a sinusoidal nature
• amplitude of a vibration - the maximum displacement of an object from its resting position

Motion of a Mass on a Spring

• Hooke's Law

The Nature of a Wave

Waves Lesson 1a-c 4/30/12
Waves and Wavelike Motion

• waves have a sinusoidal nature
• crest and trough
• many types of waves
• two most common types of waves - sound waves and light waves

What is a Wave?

• equilibrium position - rest position
• pulse - a single disturbance moving through a medium from one location to another location
• wave - the repeating and periodic disturbance that moves through a medium from one location to another
• medium - substance or material that carries the wave
  • collection of interacting particles

Categories of Waves

• transverse wave - a wave in which particles of the medium move in a direction perpendicular tothe direction that the wave moves
• longitudinal wave - wave in which particles of the medium move in a direction parallel to the direction that the wave moves
  • ex: the waves that travel along the surface of the oceans
• waves traveling through a solid medium can be either transverse waves or longitudinal waves
• surface wave - a wave in which particles of the medium undergo a circular motion
  • neither longitudinal nor transverse
• any wave moving through a medium has a source
• electromagnetic wave - wave that is capable of transmitting its energy through a vacuum
  • produced by the vibration of charged particles
• mechanical wave - a wave that is not capable of transmitting its energy through a vacuum
  • requires a medium in order to exist

Behavior of Waves

Waves Lesson 3a-d 5/4/12
Boundary Behavior

• boundary behavior - the behavior of a wave (or pulse) upon reaching the end of a medium
• boundary - interface of the two media
• fixed end reflection - ex: end of a rope
• incident pulse - pulse that is introduced at one end of a medium and ends at the other end of the medium
• reflected pulse - disturbance that returns to the left after bouncing off something
  • speed of the reflected pulse is the same as the speed of the incident pulse
  • wavelength of the reflected pulse is the same as the wavelength of the incident pulse
  • amplitude of the reflected pulse is less than the amplitude of the incident pulse
• free end reflection

Reflection, Refraction, and Diffraction

• law of reflection - the angle at which they approach the barrier equals the angle at which they reflect off the barrier
• reflection - involves a change in direction of waves when the bounce off a barrier
• refraction - involves a change in the direction of waves as they pass from one medium to another
• diffraction - involves a change in direction of waves as they pass through an opening or around a barrier in their path

Interference of Waves

• wave interference - the phenomenon that occurs when two waves meet while traveling along the same medium
• constructive interference - type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction
• destructive interference - type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction
• principle of superposition - when two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at the same location

The Doppler Effect

• the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding

Standing Waves

Waves Lesson 4a-e 5/7/12
Traveling Waves vs Standing Waves

• traveling wave - type of wave pattern that is seen traveling through a medium
  • observed when a wave is not confined to a given space along the medium
  • ex: ocean wave
• standing wave pattern - characterized by points that appear to be standing still
  • points vibrate back and forth from a positive displacement to a negative displacement
  • vibrations occur at regular time intervals such that the motion of the medium is regular and repeating - a pattern is readily observable

Formation of Standing Waves

• standing wave pattern - vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source
• harmonics - frequencies of vibration that such patterns are created within

Nodes and Anti-Nodes

• node - point along the medium that appear to be standing still
  • points that undergo the maximum displacement during each vibrational cycle of the standing wave
• antinodes - opposite of nodes
• should not be confused with crests and troughs

Harmonics and Patterns

• standing wave patterns can only be produced within the medium when it is vibrated at certain frequencies
• harmonics - these frequencies and their associated wave patterns
• first harmonic - simplest wave pattern produced when vibrations were produced into the end of the medium at low frequencies
• second harmonic - pattern with three nodes and two antinodes

Mathematics of Standing Waves

• harmonic number - equal to the number of antinodes in the pattern